A368871 Number of compositions (ordered partitions) of n into odd parts not greater than sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 40893, 64208, 100816, 158296, 248548, 390257, 612761, 962125, 1510678, 2371987, 3724369, 5847808, 9181920, 14416967, 22636762, 35543051

Offset

0,10

Links

Table of n, a(n) for n=0..40.

Maple

b:= proc(n, t) option remember; `if`(n=0, 1, add(
     `if`(j::odd, b(n-j, t), 0), j=1..min(n, t)))
    end:
a:= n-> b(n, floor(sqrt(n))):
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 13 2024

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[OddQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 40}]

Crossrefs

Cf. A000045, A364526.

Sequence in context: A279771 A257043 A369341 * A120144 A255924 A067452

Adjacent sequences: A368868 A368869 A368870 * A368872 A368873 A368874

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 08 2024

Status

approved